Properties

Label 15.30
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 6.842939
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(6.84293956587284457522059080612 \pm 6 \cdot 10^{-11}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -0.05637735 \pm 8.2 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.99682159 \pm 8.2 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.03254948 \pm 9.2 \cdot 10^{-8} \)
\(a_{7}= +0.50490461 \pm 7.1 \cdot 10^{-8} \) \(a_{8}= +0.11257551 \pm 5.9 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.02521272 \pm 9.2 \cdot 10^{-8} \) \(a_{11}= -1.24883556 \pm 7.1 \cdot 10^{-8} \) \(a_{12}= -0.57551522 \pm 9.2 \cdot 10^{-8} \)
\(a_{13}= -0.81178682 \pm 7.1 \cdot 10^{-8} \) \(a_{14}= -0.02846518 \pm 8.4 \cdot 10^{-8} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.99047489 \pm 6.9 \cdot 10^{-8} \) \(a_{17}= -1.54252199 \pm 6.2 \cdot 10^{-8} \) \(a_{18}= -0.01879245 \pm 9.2 \cdot 10^{-8} \)
\(a_{19}= -1.48461354 \pm 6.2 \cdot 10^{-8} \) \(a_{20}= -0.44579217 \pm 9.2 \cdot 10^{-8} \) \(a_{21}= +0.29150681 \pm 8.1 \cdot 10^{-8} \)
\(a_{22}= +0.07040604 \pm 8.6 \cdot 10^{-8} \) \(a_{23}= -0.71489842 \pm 5.5 \cdot 10^{-8} \) \(a_{24}= +0.06499550 \pm 7.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.04576639 \pm 9.2 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.50329982 \pm 9.2 \cdot 10^{-8} \) \(a_{29}= +0.64001945 \pm 4.5 \cdot 10^{-8} \) \(a_{30}= -0.01455657 \pm 9.2 \cdot 10^{-8} \)
\(a_{31}= +0.73240322 \pm 3.7 \cdot 10^{-8} \) \(a_{32}= -0.16841585 \pm 6.2 \cdot 10^{-8} \) \(a_{33}= -0.72101555 \pm 8.2 \cdot 10^{-8} \)
\(a_{34}= +0.08696330 \pm 7.9 \cdot 10^{-8} \) \(a_{35}= +0.22580021 \pm 8.1 \cdot 10^{-8} \) \(a_{36}= -0.33227386 \pm 9.2 \cdot 10^{-8} \)
\(a_{37}= -0.97343398 \pm 5.3 \cdot 10^{-8} \) \(a_{38}= +0.08369857 \pm 6.9 \cdot 10^{-8} \) \(a_{39}= -0.46868534 \pm 8.1 \cdot 10^{-8} \)
\(a_{40}= +0.05034530 \pm 7.0 \cdot 10^{-8} \) \(a_{41}= +0.64206018 \pm 6.3 \cdot 10^{-8} \) \(a_{42}= -0.01643438 \pm 1.6 \cdot 10^{-7} \)
\(a_{43}= -1.31046163 \pm 6.8 \cdot 10^{-8} \) \(a_{44}= +1.24486625 \pm 6.7 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.04030408 \pm 4.1 \cdot 10^{-8} \) \(a_{47}= +0.98616248 \pm 8.2 \cdot 10^{-8} \) \(a_{48}= +0.57185094 \pm 7.9 \cdot 10^{-8} \)
\(a_{49}= -0.74507133 \pm 5.3 \cdot 10^{-8} \) \(a_{50}= -0.01127547 \pm 9.2 \cdot 10^{-8} \) \(a_{51}= -0.89057548 \pm 7.3 \cdot 10^{-8} \)
\(a_{52}= +0.80920663 \pm 7.3 \cdot 10^{-8} \) \(a_{53}= +1.09356078 \pm 8.8 \cdot 10^{-8} \) \(a_{54}= -0.01084983 \pm 9.2 \cdot 10^{-8} \)
\(a_{55}= -0.55849624 \pm 8.2 \cdot 10^{-8} \) \(a_{56}= +0.05683989 \pm 6.1 \cdot 10^{-8} \) \(a_{57}= -0.85714203 \pm 7.2 \cdot 10^{-8} \)
\(a_{58}= -0.03608260 \pm 6.0 \cdot 10^{-8} \) \(a_{59}= -1.10337684 \pm 5.8 \cdot 10^{-8} \) \(a_{60}= -0.25737823 \pm 9.2 \cdot 10^{-8} \)

Displaying $a_n$ with $n$ up to: 60 180 1000